Understanding Linear Inequalities

The video tutorial explains how to solve linear inequalities in one variable, using inequality notation, interval notation, and graphing. It highlights the importance of reversing the inequality symbol when multiplying or dividing by a negative number. Two examples are solved step-by-step, demonstrating the process of isolating the variable, solving the inequality, and representing the solution graphically and in interval notation.

What is the key difference between solving linear equations and linear inequalities?

• Linear equations and inequalities are solved in the same way without exceptions.

• Linear inequalities do not require any special rules.

• Linear equations require reversing the equality symbol when multiplying or dividing by a negative.

• Linear inequalities require reversing the inequality symbol when multiplying or dividing by a negative.

Why must the inequality symbol be reversed when multiplying both sides by a negative number?

• To simplify the equation.

• To make the inequality false.

• To maintain the truth of the inequality.

• To change the variable's sign.

In the first example, what is the solution to the inequality -4x > 12?

• x > -3

• x = -3

• x ≤ -3

• x < -3

How is the solution x < -3 represented on a graph?

• An open point on -3 with an arrow to the right.

• A closed point on -3 with an arrow to the left.

• A closed point on -3 with an arrow to the right.

• An open point on -3 with an arrow to the left.

What is the interval notation for the solution x < -3?

• [-3, ∞)

• (-∞, -3)

• (-∞, -3]

• (-3, ∞)

In the second example, what is the solution to the inequality -3x ≤ -12?

• x ≥ 4

• x ≤ 4

• x > 4

• x < 4

How is the solution x ≥ 4 represented on a graph?

• A closed point on 4 with an arrow to the left.

• An open point on 4 with an arrow to the right.

• A closed point on 4 with an arrow to the right.

• An open point on 4 with an arrow to the left.

What is the interval notation for the solution x ≥ 4?

• [4, ∞)

• (4, ∞)

• (-∞, 4)

• (-∞, 4]

What happens to the inequality symbol when dividing both sides by a negative number?

• It becomes an equality symbol.

• It remains the same.

• It is removed.

• It is reversed.

What is the purpose of using interval notation in inequalities?

• To check the solution.

• To represent the range of solutions.

• To solve the inequality.

• To graph the inequality.